How to scale a mesh evenly without causing the faces to intersect?
ALTS is to scale along the Normals and if your vertices are all on the same plane they should only move up and down. If not, select all and scale the Z axis to Zero, and then remove doubles - just to keep things simple.



You could start by trying to scale the model just on the X axis and then the Y and see where the distortion starts. After that you will probably need to proportional scale - and it might be handy to turn on connected. You can also move and rotate proportionally.



What you might be thinking when you say 'scale evenly' is probably more correctly offsetting. There are tricks and work-a rounds but most software I have come across runs into trouble with intersecting surfaces.